Admittance Matrix Research Articles

A general analysis method of transmission lines faults response with all frequency components under new energy

Nowadays, a large number of photovoltaic power stations have been connected to the grid. As the control algorithm of photovoltaic power generation often uses Maximum Power Point Tracking (MPPT), the electromagnetic transient process generated by frequent regulation process is gathered into the transmission network. And long transmission lines need series compensation which also causes electromagnetic transient process. Since the sampling frequency of the protection device was not high enough in the past, the recorded waveform could not reflect the actual situation. In particular, because some high-frequency harmonics could not be observed, the harm brought by them did not attract enough attention, and the adverse effects gradually increased. In this paper, the transient response of faults in transmission lines can be accurately calculated by a method, which combined with the phase component method and the Laplace transform. According to the topological relationship of transmission lines, a frequency domain model considering the initial energy storage is given. Whether the system parameters are symmetrical or not, the model can accurately calculate the transient response. Besides, various faults are described by modifying the node admittance matrix. And the system response that includes all frequency components in the time domain are obtained by the inverse Laplace transform. In the case of a simple transmission system, the calculation results are compared with those obtained with the ATP/EMTP. Such comparisons validate the effectiveness and accuracy of the method. The method can accurately reflect all transient components at different frequencies caused by faults or disturbances, and it is suitable for both transient studies and steady-state analysis.

Cable Modeling for Very Fast Transient Simulation Studies Using One-Sided Voltage Transfer Function Measurements

A novel measurement-based method for high-frequency modeling of shielded cables is introduced for use in very fast transient simulation studies. The method requires measurements on one cable end only, thereby being applicable to installed cable systems. Three frequency sweep voltage transfer measurements are performed at one cable end using a vector network analyzer (VNA) with gain-phase setup, two voltage probes and one series resistor. From the measurements is calculated the cable 2 × 2 admittance matrix as function of frequency where a sign arbitrariness is removed using a local rational model that is swept along the frequency samples. The resulting admittance matrix can be fitted by a lumped-parameter rational model, or be subjected to modeling by a frequency-dependent traveling wave model which also permits to change the cable length. Application to a 150 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> single core cable of 252 m length demonstrates that the model reproduces measured cable high-frequency damping effects that result in sub-microsecond voltage rise times. A classical modeling approach based on skin effect formulae gives too little damping.

A Novel Modeling Approach for Wavelet Reconstruction Processors Using Surface Acoustic Wave Devices

Wavelet reconstruction processors (WRPs) using surface acoustic wave (SAW) devices are a simple and efficient implementation of inverse wavelet transform technology in practical industrial applications. To assure the accuracy of the device fabrication, this article proposed a new model of WRPs based on the channel division approach and the two-port electrical network after investigating the Delta-Function Model (DFM) of interdigital transducers (IDTs), which can easily analyze the bandwidth, the admittance matrix, transfer function and insertion loss for an IDTs and a WRPs. Furthermore, to validate the simulation effect, some samples of WRPs were successfully manufactured with ST-X quartz as the piezoelectric substrate and Al thin film as the IDTs material, the center frequency and the scale are 49.0 MHz and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{-{2}}$ </tex-math></inline-formula> , respectively. A comparison of the experimental and simulation results reveals that the model possesses high accuracy with the relative error operating frequency of 0.204%, the relative error in insertion loss less than 1.17% at the operating frequency. This work provides an effective model for WRPs with higher precision, low consumption, high operation speed, making it possible for the acceleration of the development process of the WRPs for large-scale application and commercial promotion.

External Identification of a Reciprocal Lossy Multiport Circuit under Measurement Uncertainties by Riemannian Gradient Descent

The present paper deals with the external identification of a reciprocal, special passive, 2n-port network under measurement uncertainties. In the present context, the multiport model is represented by an admittance matrix and the condition that the network is ‘reciprocal special passive’ refers to the assumption that the real part of the admittance matrix is symmetric and positive-definite. The key point is to reformulate the identification problem as a matrix optimization program over the matrix manifold S+(2n)×S(2n). The optimization problem requires a least-squares criterion function designed to cope with over-determinacy due to the incoherent data pairs whose cardinality exceeds the problem’s number of degrees of freedom. The present paper also proposes a numerical solution to such an optimization problem based on the Riemannian-gradient steepest descent method. The numerical results show that the proposed method is effective as long as reasonable measurement error levels and problem sizes are being dealt with.

High-pass negative group delay analysis of single capacitor three-port circuit

PurposeThis paper aims to develop high-pass (HP) negative group delay (NGD) investigation based on three-port lumped circuit. The main particularity of the proposed three-port passive topology is the consideration of only a single circuit element represented by a capacitor.Design/methodology/approachThe methodology of the paper is to consider the S-matrix equivalent model derived from admittance matrix approach. So, an S-matrix equivalent model of a three-port circuit topology is established from admittance matrix approach. The frequency-dependent basic expressions are explored to perform the HP-NGD analysis. Then, the existence condition of HP-NGD function type is analytically demonstrated. The specific characteristics and synthesis equations of HP-NGD circuit with respect to the desired optimal NGD value are established.FindingsAfter computing the frequency expressions to perform the HP-NGD analysis, this study demonstrated the existence condition of HP-NGD function type analytically. The validity of the HP-NGD theory is verified by a prototype of three-port circuit. The proof-of-concept (POC) single capacitor three-port circuit presents an NGD response and characteristics from analytical calculation and simulation is in very good correlation.Originality/valueAn innovative theory of HP-NGD three-port circuit is studied. The proposed HP-NGD topology is constituted by only a single capacitor. After the topological description, the S-matrix model is established from the Y-matrix by means of Kirchhoff voltage law and Kirchhoff current law equations. A POC of single capacitor three-port circuit was designed and simulated with a commercial tool. Then, a prototype with a surface-mounted device component was fabricated and tested. As expected, simulation and measurement results in very good agreement with the calculated model show the feasibility of the HP-NGD behavior. This work is compared to other NGD-type function with diverse number of ports and components.

Inverse Power Flow Problem

We formulate an inverse power flow problem that infers a nodal admittance matrix from voltage and current phasors measured at a number of buses. We show that the admittance matrix can be uniquely identified from a sequence of measurements corresponding to different steady states when every node in the system is equipped with a measurement device, and a Kron-reduced admittance matrix can be determined even if some nodes in the system are not monitored (hidden nodes). We propose an effective algorithm to uncover the actual admittance matrix of a radial system with hidden nodes from its Kron-reduced admittance matrix.

Advanced Synthesis and Precise Design of Inline Fully Canonical Filters With High Selectivity

This article presents an advanced synthesis and novel designs of inline fully canonical filters with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> cascaded extracted pole (EP) sections, providing higher band-edge selectivity and suppressing interference from adjacent bands. The conventional fully canonical prototype is reconfigured to significantly facilitate filter design and fabrication. Moreover, to synthesize realizable circuits, a general node scaling method based on admittance matrix is implemented. All associated elements, especially the junction susceptances, can be scaled directly without the aid of inverters, avoiding intricate equivalent circuit transforms. Furthermore, the importance of precise control over the junction susceptances in filter design is discussed for the first time. Accurate junction susceptance enables the exact mapping from synthesized circuits to physical structures, preventing brute-force optimization. In particular, a new and compact EP structure in coaxial technique is proposed with flexibly tuned loading phase and accurately regulated junction susceptance. The good measurement results of a coaxial EP filter with four reflection zeros (RZs) and four transmission zeros (TZs) validate the effectiveness of the proposed theories. Also, this is the first reported coaxial fully canonical filter with only build-in capacitive couplings to avoid passive intermodulation (PIM).

Bayesian Error-in-Variables Models for the Identification of Distribution Grids

The increasing integration of renewable energy requires a good model of the existing power distribution infrastructure, represented by its admittance matrix. However, a reliable estimate may either be missing or quickly become obsolete, as distribution grids are continuously modified. In this work, we propose a method for estimating the admittance matrix from voltage and current measurements. By focusing on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> PMU measurements and partially observed networks, we show that voltage collinearity and noisy samples of all electric variables are the main challenges for accurate identification. Moreover, the accuracy of maximum likelihood estimation is often insufficient in real-world scenarios. To overcome this problem, we develop a flexible Bayesian framework that allows one to exploit different forms of prior knowledge about individual line parameters, as well as network-wide characteristics such as the sparsity of the interconnections. Most importantly, we show how to use maximum likelihood estimates for tuning relevant hyperparameters, hence making the identification procedure self-contained. We also discuss numerical aspects of the maximum a posteriori estimate computation. Realistic simulations conducted on benchmark electrical systems demonstrate that, compared to other algorithms, our method can achieve significantly greater accuracy than previously developed methods.

Modeling for Complex Modular Power Electronic Transformers Using Parallel Computing

The modular power electronic transformer (PET) faces difficulty carrying out microsecond-level electromagnetic transient simulations. This article provides a high-speed and high-precision simulation method capable of eliminating the internal nodes and reducing the order of the nodal admittance matrix. Meanwhile, the parallel computing is integrated into the whole solution process, which achieves a significant simulation speedup. A physical prototype is established to prove that the detailed model (DM) is sufficient to reflect the dynamics of physical devices. Moreover, simulations in PSCAD/EMTDC are carried out to compare the proposed method with the DM in terms of accuracy and time efficiency. Simulation results show that the proposed method is accurate to simulate the external and internal dynamics of PET with hundreds of times simulation speed acceleration.

Optimal Allocation and Sizing of Fault Current Limiters Considering Transmission Switching With an Explicit Short Circuit Current Formulation

As the power system expands with a more complex network structure, the excessive short-circuit current (SCC) has become a major obstacle to the rapid development of power system. The paper proposes a SCC-constrained planning model to determine the optimal locations and sizes of fault current limiters (FCLs) while considering transmission switching. N-1 security criterion is included to ensure that switching off lines will not jeopardize system security. One challenge is that the relationship between SCC and binary variables associated with switching states of transmission lines and activation statuses of FCLs is nonlinear and hard to obtain the exact expression. To this end, the paper begins with the equations of admittance matrix and nodal self-impedance, and derives the explicit formulation of SCC considering transmission switching and FCL activation. Based on the explicit expression of SCC, the proposed optimal allocation and sizing model of FCLs is formulated as a mixed integer linear programming (MILP) problem which could be solved by off-the-shelf commercial solver Gurobi in MATLAB. Numerical case studies on IEEE 30-bus, 118-bus and 1354-bus systems validate the effectiveness and advantages of the proposed model in reducing total costs and enhancing system security. The modeling accuracy of the explicit SCC formulation is also illustrated.

A Systematic Stability Enhancement Method for Microgrids With Unknown-Parameter Inverters

With massive electronic inverters, microgrids are threatened by the instability problems caused by the impedance interactions among inverters and the network. For the microgrids with black-box inverters (whose parameters are unknown due to industry secrets), it is hard to assess, much less enhance, the stability of such systems. This article proposes a systematic impedance-based stability assessment and enhancement method for the microgrids with black-box inverters. First, the return-ratio matrix <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">net</sub> of the system with both current-controlled and voltage-controlled inverters is formulated based on the nodal admittance matrix. And then, the sensitivities of the critical eigenvalues of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">net</sub> are calculated with respect to individual admittances/impedances of inverters, which can identify the “trouble maker(s).” Moreover, the low voltage active damper (LVAD) is proposed for the stability enhancement of the system. An eigenvalue perturbation sensitivity analysis method is presented to calculate the sensitivities of the critical eigenvalues with respect to nodal parallel admittances, which identifies the optimal installation position for LVAD, and accordingly provides the guidance for the design of LVAD. The effectiveness of the proposed method is verified using a modified IEEE 6-bus system in PSACD/EMTDC and RT-Lab platforms.

Modeling and Low-Frequency Oscillation Analysis of an Asymmetrical Traction Power System Connected to Power Grid

The traction power system is supplied by three-phase power grids in China, forming an asymmetrical system. However, current research on wideband-oscillation analysis of the traction power supply system assumes that vehicles in a feeding section are supplied by a single-phase ideal voltage source. Meanwhile, the existing vehicle impedance models are inapplicable for the stability analysis of this asymmetrical system. In this article, a single-input and single-output impedance of the vehicle is derived and the corresponding admittance can be directly used to form the system node admittance matrix and to analyze system stability by the modal analysis. The node admittance matrix of this asymmetrical system is established by putting the derived vehicles’ admittance into the node admittance matrix of two feeding section traction networks, the traction transformer and the equivalent circuit of power grids. Then, the modal analysis method is used to obtain the low-frequency oscillation modes of this asymmetrical system and to analyze the sensitivities of different parameters to the oscillation mode. The interaction between the two feeding sections and their interaction with power grids is studied. Finally, the correctness of theoretical findings is verified by simulation in MATLAB/Simulink and experiment in Starsim/HIL.

CALCULATION OF FAST FRONT OVERVOLTAGES IN VICINITY OF A POWER TRANSFORMER

During their lifespan all the primary equipment installed in power system is subjected to transients. Therefore, it is necessary to adequately dimension and protect the equipment. However, in the networks with high share of renewables, power electronics, cables or near GIS, the failure can occur even though good practice of insulation coordination are fulfilled.&#x0D; In this paper high frequency power transformer model is presented. Such model is based on measurements of admittance matrix and is adequate for simulation of fast front transient in EMTP like software. Additionally, simulations of lightning and switching overvoltages are given for the observed power transformer unit.

Two-dimensional convolution-based power system reliability assessment

With the rise in carbon emissions, it has become fashionable to construct a new power system using new energy as the primary raw material for power generation. This, however, might result in a significant rise in the number of system states and frequent changes in the system state. These issues raise the bar for the effectiveness of system dependability evaluation. Traditional evaluation procedures necessitate computing Optimal Power Flow (OPF) for many systems states one by one, which is unquestionably time-consuming. For that purpose, this research proposes a reliability evaluation approach based on two-dimensional convolutional networks. Branch circuit fault messages are analyzed with generator fault messages. Multiple channel state data from power system node admittance matrices, power generation, and energy demand are fed into a two-dimensional convolutional neural network. This is used to determine the regression connection between load curtailments and system status data and to forecast load curtailments. Finally, it is applied to the RTS-79 system, and experimental results demonstrate that the technique has certain advantages in terms of computing speed and accuracy.

Sensitivity analysis of power system small signal stability to geomagnetic disturbances

Geomagnetically induced currents driven by geomagnetic disturbances can cause half-cycle saturation of transformers and consequently affect the power grid with reactive losses. The impact of geomagnetic disturbances focuses on voltage stability, and the research object is the conventional system without considering wind power. In this paper, we study the impact of geomagnetic disturbances on the small signal stability of doubly-fed induction generators integrated systems. After the reactive power loss caused by geomagnetic disturbances and wind power output are equivalent to grounding admittances, the influence of geomagnetic disturbances on small signal stability can be transformed into its impact on the equivalent electrical distance between synchronous generators by shrinking the admittance matrix. Then, the electromagnetic power of synchronous generators is affected, and the impact of wind farm ratio and geomagnetic disturbances is incorporated into the system state equation. The results show that the oscillation frequency and damping ratio increase first and then decrease with the increase of wind power ratio when geomagnetic disturbances occur, but they are generally smaller than those without geomagnetic disturbances. The sensitivity of inter-area oscillation mode to induced geoelectric fields is higher than that of intra-area oscillation modes, and the sensitivity to reactive power losses caused by geomagnetic disturbances in substations is different, which provides a reference for further research on optimizing blocking devices placement to mitigate the impact of geomagnetic disturbances on small signal stability.

Study of black-box models and participation factors for the Positive-Mode Damping stability criterion

The dominance of power electronics in modern power systems makes it difficult to study stability with sufficient accuracy given the available information, so it is necessary to enhance current frequency-based stability methods. The positive-mode damping (PMD) criterion is a recently powerful proposed frequency domain method to study the stability of multi-infeed VSCs grid-connected networks in the nodal admittance matrix form. The integration of black-box models and the introduction of participation factors have been identified as key lines of this work for stability studies completeness. For this purpose, a case study is built in Matlab/Simulink to address the oscillatory phenomena of modern power systems modelled in the nodal admittance matrix form with the integration of black-box models. Furthermore, this study successfully tests the performance of the participation factors applied to the PMD, which have proven to be as useful as the ones of the state-space representation in a 7-bus network example.

Equivalent model for interconnected power systems based on sensitivity consistency of tie-line power

Static security analysis (SSA) is a significant measure to verify the secure and stable operation of power grids. However, it is too time-consuming to perform SSA for interconnected networks due to the scale of network. Therefore, the equivalent-based method attracts attention due to simplifying the external networks (uninteresting networks). However, existing equivalent methods are not suitable for SSA, which are based on the assumption that the topology of internal networks is invariant. This paper proposes a novel static network equivalent method for SSA in interconnected networks. The proposed method can adaptively and precisely preserve the impact of external networks on topology changes of internal networks. Specifically, based on the sensitivity consistency of tie-line power, the equivalent nodal admittance matrix is derived for the external networks. The parameters for the obtained equivalent networks are obtained by least square model with Kirchhoff and necessary logistic constraints to achieve the optimal equivalence accuracy. The accuracy and practicability of proposed method are verified by using IEEE 39-bus system and IEEE 118-bus system.

Compact Thermal Modelling of Magnetic Components using an Admittance Matrix Approach

Unlike semiconductor devices, the thermal modelling of magnetic components has not been standardized. Due to this lack of standardization in the academic community, most proposed magnetic component thermal models have not been evaluated for boundary condition independence. Hence, they cannot be classified as Compact Thermal Models (CTMs). In this study, CTMs of a PQ 30/40 inductor are developed using an admittance matrix-based approach. First, a Detailed Thermal Model (DTM) of the inductor under direct current excitation is developed and validated using experimental test results for power dissipation varying from 2.6 to 11.9 W. Following this, a single heat source CTM is developed from the DTM data using the admittance matrix approach. The thermal performance of the deduced CTM is evaluated for fifteen different boundary condition scenarios with surface heat transfer coefficients varying between 1 to 200 . The surface temperature and heat flux predictions were within 5% of the DTM results, while the junction temperature error was 10%. Most magnetic components like transformers and inductors have multiple loss sources. Hence, the DTM and CTM were re-evaluated for multiple heat sources. The resulting multi-heat source CTM was also observed to accurately predict surface temperatures and heat fluxes.

Generalized impedance model and interaction analysis for multiple grid-forming and grid-following converters

The growing use of power electronics converters in the power system leads to emerging stability issues. However, existing impedance models are insufficient for analysis of the converter-induced stability issues in the converter-congregated local area, especially faced with the hybrid integration of both grid-following (GFL) and grid-forming (GFM) converters. In this paper, a generalized impedance model in the d q frame is developed to facilitate the impedance-based analysis of any grid node with both GFL and GFM converters. With this model, closed-loop, internal and external stability performance can be accurately described and predicted. This paper shows that the internal stability of power converters has the feature of transferability. Therefore, to facilitate the internal stability analysis of multiple-input and multiple-output systems, this paper proposes a stability analysis method that utilizes the determinant of total admittance (matrices in high dimension) for direct stability demonstration, based on the recognition of instability pattern. Finally, the procedure for integrating power converters is considered to help with the stability-oriented design. The established impedance model, the proposed stability analysis method and the converter integration procedure are validated with control hardware-in-the-loop results in a study case of a multi-terminal network with current-controlled converters and virtual synchronous generators. • Impedance model describing any local area with GFL and GFM converters is proposed. • The determinant of total bus admittance is used for internal stability demonstration. • Impacts of critical system parameters on internal and external stability are studied. • A three-step procedure is adopted to facilitate the stability-oriented design.

Log(v) 3LPF: A Linear Power Flow Formulation for Unbalanced Three-Phase Distribution Systems

In this work, we introduce Log(v) 3LPF, a linear power flow solver for unbalanced three-phase distribution systems. Log(v) 3LPF uses a logarithmic transform of the voltage phasor to linearize the AC power flow equations around the balanced case. We incorporate the modeling of ZIP loads, transformers, capacitor banks, switches and their corresponding controls and express the network equations in matrix-vector form. With scalability in mind, special attention is given to the computation of the inverse of the system admittance matrix, Ybus. We use the Sherman-Morrison-Woodbury identity for an efficient computation of the inverse of a rank-k corrected matrix and compare the performance of this method with traditional LU decomposition methods using Big- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}$</tex-math></inline-formula> notation. We showcase the solver for a variety of network sizes, ranging from tens to thousands of nodes, and compare the Log(v) 3LPF with commercial-grade software, such as OpenDSS.